Optiplex 3080 Micro computer goes to sleep when dual monitors are turned off

if you turn off only one monitor (either the hdmi or DP) the pc stays awake, correct?

it is a micro, so I presume you are using wireless. 

your micro behaves like a laptop, when the lid is closed (display turned off), it turns off wireless and goes to sleep.  you can revert that in laptop, and in micro too.

someone posted a solution for this issue.  try it.

Change the power management settings of the wireless card:

1. Click on ‘Device Manager’.
2. Click the + sign to expand the ‘Network Adapters’ entry.
3. Right-click the wireless adapter and click ‘Properties’.
4. Click on 'Power Management'.
5. Uncheck 'Allow the computer to turn off this device to save power'.
6. Click on 'Ok'.

Also, change the power options for the wireless card:

1. Click 'Control Panel'.
2. Click 'System and Maintenance'.
3. Click 'Power Options'.
4. Click on 'Change Plan settings' depending on the power plan your system is using currently.
5. Click 'Change advanced power settings'. Balanced [Active] should automatically show in the dropdown box.
6. Click the + symbol in front of 'Wireless Adapter Settings' to expand the section.
7. Click the + symbol in front of 'Power Savings Mode' to expand the section.
8. Select 'Maximum Power Savings' for the 'On Battery' setting.
9. Click on 'Apply'.